Spring Constant Calculator

What is the spring constant?

The spring constant is the force needed to stretch or compress a spring by one unit of length. It is also called spring rate or stiffness. For a linear spring, force is proportional to deflection, which is Hooke's law: F = k × x. The unit is N/m, or more often N/mm in practice.

The energy stored in the spring is the area under the force and deflection line: E = k × x² / 2.

Springs in series and parallel

Springs joined end to end act in series. Each carries the same force, the deflections add and the system gets softer: 1 / k = 1 / k₁ + 1 / k₂. Springs side by side act in parallel. Each deflects by the same amount, the forces add and the system gets stiffer: k = k₁ + k₂.

Rate of a helical spring

The rate of a helical spring wound from round wire follows from its dimensions: k = G × d⁴ / (8 × D³ × N_a), where d is the wire diameter, D the mean coil diameter, N_a the number of active coils and G the shear modulus of the wire. Because wire diameter enters to the fourth power, 10 percent thicker wire makes the spring about 46 percent stiffer.

Example

A spring that shortens by 25 mm under 200 N has a rate of 200 / 25 = 8 N/mm and stores 2.5 J. Two springs of 10 and 15 N/mm give 6 N/mm in series and 25 N/mm in parallel.

Limits

The calculation is for linear springs within the elastic range. It stops being valid when the spring goes solid or the wire starts to yield. For wire stress see the compression spring calculator.